analytic philosophy is modernism - this has been brought up every class atp it’s ok 😊
Frege - renewing philosophy through a better understanding of mathematics.
Formal logic is a tool for the philosopher to free themselves from the misconceptions of natural language.
Frege’s system allows setting signs and constructing their own language based on them.
Basically just basic formal logic in this. A → B, A |= B; and so on.
A. N. Prior
Prior comes up with Tonk; use introduction rules for OR, and use elimination rules of AND.
I.e., “p” allows for “p tonk q”; “p tonk q” allows both “p” and “q”.
Thus, inferentialism cannot be meaningful.
can you speak about the soundness or validity of an inference from outside a logical system?
The normativity of logic:
Analyticity is Frege’s answer to selecting between different logical systems;
Also truth-preserving is important potentially. ← a good system of axioms shouldn’t take us from something true to something false.
Subtle foreshadowing pays off (Godel)
Select any set of axioms GAMMA you want, provided that they do not allow an untrue formula A to be inferred (they do not include something like tonk)
We can construct a formula A that is true but cannot be deduced from these axioms.
- Formula A is constructed in relation to the set of axioms GAMMA such that it says of itself that it cannot be deduced from GAMMA. In other words, A is true iff A cannot be deduced from GAMMA.
- Suppose that A is not true. It follows from 1. that A can be deduced from GAMMA. So, an untrue statement can be deduced from GAMMA.
First incompleteness theorem
Not everything that is true can be formally deduced.
Tarski
Wants to give a formal definition of ‘is true’ that corresponds with everyday usage.
let the following sentence define “s” : “s” is not true; then paradox.
paradox because (T) (T-convention) is in English and English is ‘semantically closed’
Solution: different levels of / a hierarchy of languages:
- object-language that we speak about (things in) the world
- metalanguage in which we speak about the object-language
→ define truth in the metalanguage
object-language is Dutch: “Sneeuw is wit”
metalanguage is English: “Sneeuw is wit” is true-in-Dutch iff snow is white
’s’ is true-in-Dutch iff p.
Frege (again)
Develops the common picture about the meaning of sentences.
Frege discovers why it’s not trivial to discover that 3 + 4 = 7 (because it gives you more information through the sense)
Russell and Strawson deal with expressions like “the first chancellor of the German Empire”
= Definite descriptions (Russell)
= expressions that can be used to uniquely refer (Strawson)
- sentences constructed with such expressions:
- the first chancellor of the GE was an astute diplomat
- Helder de Schutter is the dean of the HIW
- …